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Al Memo 356 Logo Mema 22 

Lego Progress Hep-art B73-1&15 

H. Abolson 

J. Bamberger 

I. Goldstein 

S, Pspert 

September 1375 
Revised March 1975 


Over' the past two years, the Logo Project has grown along 
many dimensions, This document provrdes an overview in outline 
form of the main activities and accompli ehrmir's oMhe past as wofl 
as the major goal* guiding cur currant research. Research on the 
design of learning environments, the corresponding development ot 
a theory of learning and the exploration of teaching activities in 
these environments is presented. 

The work reported in this paper was supported hy the National Science Foundation 
under grunt number EC-407CBX and conducted at the ArHFkul Intelligence Laboratory. 
Massachusetts Institute of Tecbnolcgy, Cambridge, Massachusetts. 

■ Th* views and conclusions {oniAined in (.his paper are those of the author* and should. 
not be interpreted as nec«.iarlty representing the official: policies either expressed ur implied of the 
National Science Foundation or the United State* Government. 


1. Building Ne-w Learning Environment* 

lit Educational Devices 

1.1.1, Light-Sensing turtles 

1.1.2. Digital Logic 
|,|.3. Echo-location 

1.1.4, Operational Amplifiers 

1.1.5, Terminals for Vtiy Young ChiSdrrn 
).i£. Light Sensing Plotter 

1.1.7. Electric Trains 
1.1.3, 'TV Display* 

1.1.6, Remote display* 

1.2 Computer Systems 

1.2.1. The SITS Timesharing System 
1.2.2 Modifies Horn tn the Logo Lv.^.w^ 

1.2.3, Research an New Animation Systems 

1.2.4. Developing n, Design Tot a New Computer 

1.3 Research on Computer Languages 

1.5.1. Logo Subsystems 

I JJJ. Tfoi Teach System 
I.3J-2- The Fasti? System 
1.3.15. Pattern Matching 
LS.1.1- Parallel Processing 

L3& Developing Ideas for a New Computer Language 
[.3/2.]- Intelligent Mormon 

1.3.22. Actor Semantics 

1.5.23. Linguistic Implicailons oF * Graph ies-Raseci System 

1.4 Bridge Activities 

1.4.1. Physical Skills 

1.4.2. Crafts 

US Gun Is for 1975-76 

2. The Theory Behind the Environments 

2.1 Mathematics 

211 Turtle Geometry and: Differential Geometry 
2,1.2. "Eye Turtle Navigation" and Cpprdinate Systems 
■2.1.3. Signal Processirig L Function and Operators 
2.1.4. PIo(Wt4 and Pattern Recognition 
2.13. "Ccrmland" and Geometry on a Crid 

2.1.6. Differential Games and Parallel Processing 

2.1.7. Turtle Geometry and Number Theory 


2.2.1. Orbiti 

2.2.2- Color 
t3JL Sound 
2-2+. Qualitative Phyucs, 

2-1 Biology 

23.1, Tropismi 

23.2. Logomefia 
23.1. Morphology 

Z4 Music 

2.41 IriiighCi into the Learning Process 
£.4.2 Representing Musical Events 

2.5 Garoei and Simulations 
2.51 Orbit System 
y.h.% Da Site Dart 

2-5 Language- • 

2.7 Goals for 1975-76 

3l Experimenting with Learning Environments 

3.1 Overview of Teaching W74-/5 

3.2 Interaction* wjth Ftagetian Psychology 
3-ATht N*V* Learning Laborarnry 

3-4 Wort with Older Studenu 

3.4.1. High School Students. 

3.4.2. Coll* g* Undergraduates 

3.4.21 Mathematics Music . 

3.423- Computation in ihe Undergraduate Curriculum 

&5 Experiments in Learning 

3.5.1. ThermodfrtaroLLS Seminar 

3.5.2. En formal T Inn king Seminar 

3.S Teaching: Experiments. 

3.61 Developing a Better Vocabulary for Planning and Debugging 

5.6,2. "Geometry on a Grid h as an Att-er native [niraduction to Logo 

15.3. Amroal Behavior 

3.&.-t. String Figures Modifying Procedures and 'Systematic Changes" 

3.&.& Frame* oF Reference 

9.6.7. A Ptythology Lib for (tids 

3.6.8. Assembling Picture* out of Parts 

Log* Progress fit purr 

The basic [heme nf the Logo Project is the design of new learning envtronmenls. Thl* 
endeavor is grounded in both theory and experiment The theoretical foundation 15 si new 
approach to understanding knowledge and learning based on the computational paradigm. This 
novel view of psychology and epistemolngy hii ted to bath rhe construction of devices that support 
a far more active learning environment a* Well as the reformulation of curricula in way* TTIOr* 
consonant with the nature of learning 

The experimental activity involves designing teaching and teaming; activities around 
these environments with students of different ages and backgrounds. Feedback from these 
experiments it vnal to the debugging of the learning environment and of the underlying 
pedagogical theory. 

- The overview provided in this report IS organised Jnio an outline with the ma ior 

I- Building Learning Environ men:-; 

2 The Theory Behind the Environments 

A- Experimenting with Learning Environments, 

We hope that this division into separate headings does not result in a distorted impression- of our 
work: U is crucial to our intellectual approach that we do not separate the design of computer 
devices from the development of new content areas, nor the creation of educational computer 
language* from careful instigations, into the nature of knowledge and learning. For the purposes 
of this report, however, we have divided things up m precisely this way in order to more clearly 
highlight specific aceqmphihments and goals. (For j general description of the project 1 ! goals, the 
reader is directed to the original prnpgsa.1 The Uses of Technology to Enhance Education," 
published as M.IT. Artificial Intelligence M emc m) 

The sections of this report are modular and the reader is Invited to use the table of 
contents as a guide fo: ch nosing those sections which are of greatest interest. 

L Buildi ng New Learn in g Envtfcnmenls 
1.1 Education a! Da vice a 

Two years ago, the Logo project hid developed a collection of mobile turtles, some with 
touch sensors, a music box and several lcif>ds. of graphic displays. During the two years, tew 

kinds of devices have been constructed. These are listed below. 

1.1.1 Light - Sensing turU as 

The first version of a swing eye turtle was designed during I97MV7* by T. Callahan and 
D, Alpcrt. A single photo cell was coupled to con [rabble mirrors "to alfow the turtle ta direct iti 
light in different dtrecTLom and different inclinations without actually moving. Experiments with 
this turilt red to projects dealing with feedback and coordinate jystems {discussed in section 2.1.2 
below). During 1974-1973. we also began *ork on a second 'generation "eye turtle" which 
incorporates an automatic canning mechanism and a linear retina, and we Expect this device to 
provide a Fgrum for teaching about signal processing and functions (See action 213 ). A goal for 
1975-igfle 11 to complete construction of thll device and to develop the associated projects. 

1.1-2 D ig ital Logfc 

During I573-J974, we explored the realm of digital logic design as a new domain in which 
students could explore fundamental cognitive ideas. A project which illustrated this was that of 
deigning "turtle ears", This project allowed the student to address in an active way concept! 
which involve, on one hand, the nature of problem solving, planning and debugging, and on the 
other, the physics of sound and the nature of time. Preliminary w or k has been done to mate this 
domain accessible to ;tud<flu by designing digital logic lab stations that can tint with the Logo 

A goal ror 1S7S-197& is to complete the design of iuch stations and continue the 
development of this project area with itudents. 

1,1,3 Echo location 

The work On "turtle ears" mentioned above led to the construction of a "turtle bat" which 
Ut lilies a computer-controlled sonar system, We have not yet developed this Co a stage where it can 
be conveniently used by children, but a goal for 1975-19*6 I no do so in conjunction with work on 
the physics of sound. 


LI .4 Opera t ional Amplifier s 

During 1974-1975, J, Lindquist began work on a different area of electronics based on 
mating operational amplifier* conceptually and materially accessible :d young students. This haj 
resulted, in the development of a fust H op amp construction tit" A goal for 1975-1976 will be to test 
this kit In a variety of teaching situations. 

M,5 Terminals for Very Young Ch lfdren 

For some years we have esperirmnted (with Special conrrol devices such a; the "button 
box," designed and built by K. Perlman, one of our graduate research assistant). This, it a 
computer input device whkh has keys for turtle commands, numbers and the primitives 'needed to 

create procedures. LI sing- the button box instead or a full typewriter keyboard g really improves the 
ratio of "action obtained" to 'frustratlon H for very young children. This year experiments Jit the 
f Hit gride level were much mere extensile and systematic than previously. Our ability to use (he 
button box grew substantially. So did our awareness of its limits' ions which has been translated 
into the design of several alternative Initial Ion devices. One oF these, "the slot machine/ ha* been 
built by R. Petlman in collaboration with D. Hillis, an undergraduate ai the lab, The slot machine 
allows programs to be physically constructed by placing cards in slgts. The cards are marked, with 
Visible symbols (to be read by the child) for parTitulir commands and carry corresponding 
punchout bole codes to be read by the machine. 

During I975-197G, a goal will be to interface the sloe machine with the computer arwl run 
experiments on Its merits as an introductory programming medium for the beginner. 

1.1.6 Lighl S ensi nE Plotter 

We have experimented with a nnvel way of using a plotter with a photo-diode in place 
of the pen, This provided the bad ground for a number of projects in pattern recognition carried 
out by a class of high-school students under the direction of N- Rowe, an MIT undergraduate. 

1.1.7 Electric Trains 

During 1974 -1905, .another group of high-school Students, under the direction of J. £vans h 
constructed and experimented with a "computer-controlMd transportation system" by attaching the 
twitching mechanisms in an electric tram set to our computer. 

1.1.8 'TV" Displays 

The first Logo display system involved the use of vector-display generators Such 
displays suffer from (be problem of bejng limited in the amount of picture that they can display 
before flicker becomes noticeable. The decrease in the cost of memory makes feasible an 
alternative — raster scan TVs -- that allow arbitrary amounrs oF information including patterns 
and textures to be displayed. 

Durkng 1974-I9*5 h R, Lebel completed the construction of our new raster scan displays, 
and these are currently being integrated into our computer system for use with children during the 

Coals for 1975-1976 are to design projects that taVe advantage of the capabilities provided 
for drawing solid area,j h gray scales and color. 

1,1.5? Remote Displays 

During 1974-1975, S0*n»e members 0.f our research group also parlkJpaied with M- Minsk y 
In the design of anoLhci. conceptually very different, display system. A first version Of This system 
was built and led to a thorough re-desigrt whkh Is now completed- The "Minsty' displays have 
the advantage of operating remotely over telephone lines and of serving as prototype* for the 
design Of a new educational computer {See section I.H.). A project for the coming year Is to 
construct prototypes for incorporation into the Logo system and experiment with their Unique 
capabilities for educational application i- 

1.2 Computer Systems 

L2.1 The SITS Time sh aring System 


Originally Logo was implemented in assembly language an the PDP-IO. In order to 
provide a computer syscen dedicated to educational us*, it was adapted for the PDP-11. Tbi ftttt 
milestone in Chit direction was the completion in 19^3-1971 of a dedicated timesharing system 
running ULOGO 

This was not an entirely satisfactory solunon because of the inability of the system to be 
self-ma in taming or to run wher languages or special purpose jobs (hie .» simulation environment 
or an educational real-time game). During hT/l-lSfa, our programming staff,. under Lhe direction 
Of R. Lebel, Completed the design and Impfemtmatlon of a general purpose multi-languag* 
t|rn*sharing system for the P DP 11/ 15. The SITS timesharing system was developed to provide an 
envffonmeni suitable for running Logo and other PDPJJ/15 programs. It incorporates a Multidt- 
like tree structured file system including (potentially) rult accesi control. It also provide* unique 
capabilities; for running: programs as multiple process systems, rather than the more common single 
process approach, and the ability for each user to run many jobs simultaneously. The system 
includes provisions for Using both the older refrEshed displays and our new raster display*, 

1.2.Z Modifications t o the Log o Language 

The Logo language has n«ver ieemed to WS to be a completed entity. Gradual evolution 
has occurred over rhe years* making the language more powerful and convivial for children. 
During ISftXSft,. SUCh features as decimal arithmetic and arrays were added- This was made 
necessary by various projects for children requiring their use 

During 1*74^75., additional modifications included extension of the filing system, the 
development of a "real-time editor" made possible by qui TV displays, and new commands to allow 
for "instantaneous response' from keyboards and switches For en ample, one can now write 
programs which cause the teletype keyboard to simulate an organ keyboard. This facility also 
came in useful in our work in physics {Section 2.5.1) and in implementing the Fastr system (Section 

A current issue is whether we now have enough experience to radically redesign the 
language. This is discussed separately below in section 13.2. 

i.2,3 Research on New Animal ion Systems 

The increased capabilities ol our TV displays, as well as the MinsLy display, has recently 

led to a f luTry Of retea-rch on extensions to Logo to provide more flexible and powerful animation 
f articles, Two rather diFferent prototype systems were implemented by H. Lieberman and D. 
HllliS. This work also leads directly to ideas about new computer languages {Section I.3-.2) and W# 
expect it to be actively pursued in [975^6 

1 2.4 Developing a Design for a New Computer 

We have become convinced ;hat the time is now ripe for designing a small but very 
powerful computer for educational use. Under Professor ltfrnsky"s direction, several rounds of 
design have been undertaken. A goal for 1973-1976 is to biing these designs to fruition in the form 
of a working model of a personal studen: computer 

1,3 Research on C omn ute r Languages 

1.3.1 Logo Subsystems 

One of "he most important syntactic differences between Lego and more commonly used 
languages like BASIC and FORTRAN is that Logo li an extensible- language . Tn other words, 
invoking a user-defined procedure is synlac" kalJy identical to invoking a system primitive. This 
makes it possible- for the classroom teach pi to sub serially modify the way Logo "appears to the 
children,* or to develop specjal putpo&e subsystem Without having EC ^eL involved wi;h systems 
programming. We have experimented with this facility in a number of different ways: Th e Teac h System 

■ C. Solomon ■ has. developed a subsystem tailed Teach and has extensively tested It in 
classroom use, When this n m ape-ration '.he beginner is prompted by the computer in the process 
of defining a new procedure. Problems of supplying line numbers and filing the ptOLfdnre away 
when it is defined are automatically taken care of by the system. These, and other features, relieve 
a nervous, beginning student of the burden of Ideas which are not on' the main line, cowards the 
moment when he can write his own procedure md see it run. The Fas lr System 

Another introductory en-vironmem for students at an even more elementary level was 
designed, implemented and extensively tested, by P Gokknberg. This Ji the Fiulr (fast turtle) 
system.- 'When it is in operation, merely pressing the 7" key on'the teletype, for example, will cause 
the turtle to move forward. After a drawing has been made in this "eteh-a-tketch mode/ the 
sequence of commands is automatically defined as a procedure which can then be usri as a module 
in constructing more complex drawing. This system proved highly successful! as an introduction to 
Logo for very young children. Pat lorn Matching 

K- Kahn, me of our graduate students, implemented a sub system incorporating into 
Logo modern computational ideas about pattern matching and generation. He then used this in 
teaching children and expanded upon previous Logo work with sentence generators and other 
linguistic processing. 

L3.L4 Parallel Processing 


A parallel processing sub system was designed by H. Abelson and implemented by a 
graduate assistant, G Clemenscm This was used m providing undergraduate math students with 
an Introduction to the theory of Differential flames (See Section ?I.E.). 

i,3 2 Dev eloping Ideas for a New Computer Language) . 

When Logo was first proposed almost ten years ago it represented an attempt to build a 
language which woukl be suitable For children and also have powerful features, of the advance 
languages of that period. In the meantime the advanced languages have forged ahead and' 
developed many features which would adu r- the power of a beginner's language, We have 

always thought of Logo as a growing entity which has gradually evolved since its first conception. 
But not all charges can be mad* in this local way. and we feel that the time hat com* to put a 
major effort into exploring new approaches to programming languages for education. 

It might be felt that thii approach is out of tooth with reality- Since Logo did not 
succeed in displacing BASIC as the almost universal computer language for schools, SUrtly 
Lntioducifi^ an even more advanced language is a fonlish notion! Thii may be true, and we do not 
suggest putting all the eggs. in the cine basket of new languages. On the other hand there are 
objective reasons for the fact that BASIC remains entrenched, and some oT these are now 
beginning to vanish. Among these reason? are: 

■ the economics of computer* which in the past placed a premLum on a 
language which could exist in a small memory 

■th* lack Of convincing demonstrations of what cnuld be dope with a more 
powerful language 

the technical difficulty of implementing new languages. 

Everyone will agree that the first of these reasons is quickly vanishing. The second reason would 
Soon dissipate if we and Others ( suc - n as Lnc Xerox group! made available in a suitable form what 
*e now Vnow. And the third we see as being Tapidly changed by advances in software generation. 

During 19^*05 we investigated new languages for education from the following 

JL3J.1 Int el It sent Monitors 

These are systems which provide direct intelligent help to the programmer in planning, 
defining, executing and debugging p raced U res. It IS clear that any system which does this must 
have knowledge about the domain for which the programs are written as well as about the 
programming process itselF. Wort in This area was initiated by T. Goldstein in hi a noc'.oral 
dissertation (1973) and continued this year by M. Miller in an MS thesis and by M. Jeffrey in a 
&.S. thesis. In I?)'75-1976, we plan to reach an important milestone in the development of these ideal 
by implementing an operational monitor on the PDP-10 In Lisp-Logo. This will serve at an 
experimental system in which to actually observe the advantages and disadvantages for children of 
a learning environment in which the computer assumes many -of the responsibilities of the Teacher. A^tor Semtnties 

This new approach to the foundations of programming languages is under active 
development by both, the Xerox group and by C. Hewitt here at MIT. Such languages seem 
particularly appropriate for control of animated graphics and, in this capacity, were explored ki a 

paper by D. Hilhs and in prototype systems by K. Kahn and R. Perlman. 

1.3.Z3 Linguistic Imp lic ations of a Grap hic s- eated System 

Almost all existing computer languages are designed to be used with teletypes. They do 
not take advantage of the capabilities for immediate visual feedback and more flexible structure 
which become possible with a graphics terminal. Ideas were investigated this year in papers by R. 
Lebel and R. Perlman, and we espect this to he an active area for future research. 


L4 Bridg e Activities 

The concept of "bridge activity" has evolved in our thinking to focus oft the idea of 
creating activities language, frjmes of reference, etc. which connect both to the computer 
experience and to the familiar informal experiences of the child, 

jAl Physical Ski fit 

Our most well-developed exampfe of bridge activities is the task of learning physical 
skills by conceptualiiing the learning process of "people procedure** by an analogy with "computer 
procedure!." In the past, we have pk peri merited with projects based upon learning to tide a Bongo 

Board, juggling, riding a bicycle, walking on stilts and riding a unity le. During the paw year, H. 
Austin has devetoped a more precise procedural description ai juggling through the MM of Video 
tapes of subjects of varying degrees of compflcnce and at various stages In the learning process, 

1,4,2 Crafts 

Another area which ihould prove profitable n providing links between a child's normal 
experience* and the computer realm is that of craft projects. During the last year, Claudette 
Bradley has explored the craft of bead trig as a medium for leaching mathematical concepts. In the 
new Learning Lab (Section 3.3), we plan to s« aside space far such activities as block printing and 
building: mobiles. 

1.5 Goals f or [975-76 

The computer devices mentioned above will be used extensively with children in our new 
learning laboratory {see Section 13) during she coming months. In addition we. will be starring 
work on a number of new devices. One is an "airplane seat" that can be interfaced to the 
computer for flight simulation. Another is a Speech generator, which can be programmed to speak 
a number of different languages as well as provide voice output for Logo programs. Others 
include a computerncon trolled ;one generator which witl be used to more thoroughly integrate our 
/work in music with our woik in mathematics and physics, and an organ keyboard which can be 
used as an input device. 

Development of our time sharing system will be limned re interfacing these devices to the 
computer. We will also be taking advantage of the system's .capabilities for filing and multiple 
Jobs, to Improve upon the Logo subsystems already developed For .example, the Teach system will 
be modified to make use of the new 'real time" editor and a stock of "library routines" will be 

Ws will be trying out a number of different graphics systems over the coming year, In 
order to find better ways to make use of color, shaded drawings and faster animation. In addition 
we plan to interface a tablet in the system in nrdei to allow for graphics input. The deeper 
questions mentioned above, such as actor semamics. intelligent monitors and truly graphics-based 
languages, will be tentatively explored m implementations on the PDF-IO and writ form the basis 
for an advanced seminar at M IT jn the Spring. 

2. The Theory b&hind the- Environments 

Logo research in deigning; new learning environments has always grown from two 
intellectual Eourcei. the first, is the. application of advanced computer technology to education and 
the second is an evolving 1 theory of knowledge and intelligence based on a computational 
paradigm. The study of this theory is called Artificial Intelligence Though this title is something of 
• miinoffler White it reflects the historical origins nf the field in using (WKhmes as a laboratory 
for testing theories of intelligence, it falls to Indicate- chat the study is essentially "theoretical 
psychology," i.e. the construction of possible- theories of intelligence, 

Logo research seeks to adapt those thrones of mielhgence that are suitable for peopk at 
guidelines for the design Of education. This has consequences for the discovery at f undamcTPtll 
Characteristic! of learning as well as the specific Organisation or a subject tooplimiie learning. 

The reader is referred tu a recent pape* entitled "Artificial Tntelligence, Language and 
Education" by Papert. Goldstein and Mint*.? for a deeper study of these questions. A continuing 
goal for 1975-1976 Li to extend our understanding of learning and intelligence from an At 
• standpoint in order to develop new educational insights and applications. 

The following subsections describe specific curriculum areas where- we have made 
progress in reformulating the content to assume a more active computational form. 

2.1 Mathematics 

In IS'H-TS we continued our search' for way* to make mathematical more intuitively 

accessible to young students Progress was achieved both by examining the implications of new 
computer controlled devices as well at by taking a deeper look at some of our previous work. 

2.JA Turtle Geo metry and Differential Geometry 

In our proposal we outlined sorre theorems in our newly developed subject of Turtle 
Geometry, One very important one is the Total Turtle Tup Theorem" if the turtle follows a 
program and ends up in the same position from which it started, then, during the program, the 
turtle's heading changes by a multiple uf 360 degrees This theorem is true in the plane, but it 
would he false if rhe turtle were moving, say. on the surface of a sphere. This observation 
provides the basis for an intuitive Turtle Geometry approach to modern Differential Geometry- 
curvature, geodesies, spherical geometry, the Gi.USS-'&onnet Theorem, and SO on. H. Abel son and 
A. dlSeisa presented this material this summer In a series of tenures for high-school students. (A 
paper by diSessa, which gives an extensive treatment or this topic, currently exists in draft form 
and will shortly be completed,} 

2.1.2 "Eye> Turtle Navigation" arid Coordinate Systems 

Consider the following pTOjett The eye turtle is placed in a rectangular room. There is 
a light at each corner of the room. The turtle 'nonces where it is" by measuring the observed 
*ngks between :he lights. Now we move the turtle 10 another spot. How tan the turtle find ku 
way back to the ortginal position? 

There are two very different ways to approach this problem One Is via trigonometry 
and standard ttiangulation techniques to transform the angle data into Cartesian coordinates 
Another way to proceed goes something like this: "Look, there is nothing sacred about De*cartei' 

coordinate system, Why ant 1 mike up a better one more wiled to the problem? How about 
uilflf tfaanglts Mtrruelvft m toaidinates?" This was explored by a number of student^ including 
a high school class run by N. P. owe; also, two graduate students at The Lab.. J. CatfcffWCkl ihd tJ. 
Tunnr. developed feedback algorithms for navigating in the "angle coordinate system* which are 
sultabfy elementary for presentation to children 

2.L 3 Signal Pr oc essing, Fun d i ons and Op erators 

in our work with the eye turtle, however, ir beam* erear that a much more routing way 
to use this device was to worl wuh a ?60 degree radar-like scan of the turtles surroundings. Thrs 

prompted the de&Lgn of a setOfld^gcneratdon eye turtle which is now almost completed, and w e 
eapect thii to lead to many new projects. For example, tht data read m by the eye is "noisy,* and 
the signal must be moot. ltd. In looking for ahj«rs we are probably more interested in gradient* 
than in intensities -- the signal must be differentiate! We think that such projects will provide 
very concrete and accessible image! for runctit^ and opeyaliuns on Functions, and we plan to 
begin work on this as soon as the new turtk Is ready. 

2AAP\o\i er a and Pattern Recognition ' 

Mounting a photo-diode in plate of the pen on one of our plotters proved a convenient 
way for children ro try their hands it pattern recognition techniques. The diode is moved using 
th* normal plotter command 1, but instead of drawing a line, the student can ask if the "pen" is 
currently On a light or dark area or whether it crowed a line during its last move. Some of the 
projects undertaken by a group or high school students were developing programs to follow ».1ong 
lines and turves, dtstinguishing between various figures, and "reading" handwritten Morse cod*. 

Z.L5 "Ge rrnl and" and G eo metry on a Grid 

A very d iff fit en-, approach to geometry was further explored by L Coldttein in 
"Germland," a subsystem of Ujp-Logo. Unlike turtles, "germ*" live on a grid and when they move 
they can only move north, south, eajt or vrest. But there can be lots of germs, all moving at onte, 
foraging f Qr f«d or chafing one another. This forms a background for a number of project* 
merging ideas from ecology, game theory and automata theory, and we will continue development 

2.1.6 Differential G e rnes and P ar a ll el- Pra cesain g 

One outgrowth of the germland idea was a PDPUrLogo subsystem for parallel 
processing. This was used by a cfass or MIT freshmen to mitigate problems in the theory of 
differential game*. They wrote Logo programs io-rest various "chase-evade" strategies, explored 
the classical "lion and man" problem and the 'ABM missile" problem. 

2.1.7 Turtle Geom e try and N um ber Theor y 

Almost everyone exposed to Turtle Geometry quickly invents thr "Poly" program 
Illustrated in our proposal. But let's explore Poly. What is needed to make the program draw a 
five-jided figur*, a nine-pointed -Star? How many points will there be if we use a FiH degree angle? 
What happens when we begin to modify the program? Starting from questions like these- we soon 
find ourselves in new mathematical territory, a subject combining geometry, number theory and 
theory of compuiatlon. Questions range from being suitable for children to forming bases for 
ambitious projetts at the college level. The- were discussed this year in a working paper by H. 


2.2 Physics 

2.2.1 Qrbtts 

The sheory of planetary orbits outlined in -our proposal wis extended by H. Abelson. A, 
diSeisa and L. Rudolph Into a complete introduction :a this subject, including a qualitative 
approach fo first order perturbation theory This was published m the July 19^5 unie of Tte 
AmtrUdn Jeutnal of Fhytia and also provided rhe theoretical background for an orbit simulation 
program discussed below (Section £.5.1). 

2.2.2 Color 

We are anxiously awaiting the installation of our new projecting color TV console 
during the coming month. Anricipated projects will deal with color mixing;, spectral theory and 
optical illusioni involving color vision. 

2.2.3 Sound 

Our proposed work in spectral theory should also dovetail nicely with presets in the 

generation of rounds, This will ahso be linked iwitn work In music as well as with ecbolocatlon 
projects mentioned above (Section 1.1.2). 

Z2.4 Qualitative Physics 

The. above work has sparked a general interest in what might be called the theory of 
"qualitative physics* Thii involves investigating knowledge used tn solving physics prab ferns, 
beyond what is classically formulated in equations. Specific projects last year included a completed 
M.S. Thrsis, "Qualitative and Quantitative Knowledge in Classical Mechanics* by J. deKleer, and 
some preliminary work by H- Lin on problems in understanding thermodynamics. 

Z3 Biology 

2. 3.1 Tropisms 

The sketch on tropisms outlined in the proposal waj extended by H. Abe-lson io work 
with MIT freshmen. This, was another factor in the development of the parallel-processing iystem 

mentioned above {Section 2.1.6). 

2.3.2 LogamKia 

Thinking about tropisms also led to work on the theory of "Logemecia." a combination 
of biological considerations about tropisms and iuneses With more mathematical notions of 
feedback and scalar and vector fields S Papett and C- Solomon djd work in this area with 
children at the Martin Luther King School in Cambridge. 

Z3-3 Morphology 

Improved graphics and animanon facilities in IS^-1975 stimulated work OH procedural 
Insights Into [he shapes and movements at living things A program developed by B. Dahell 
demonstrated, how simple mechanisms could account for [he evolution- of animal horn *, Dal fell 
and H. Lieberm'an have also begun work cm a simulated "build-an-animal-kit," This allows; 
students to assemble new animals out of pre-programmed modules such as The head of a carnivore. 
the body of an herbivore, various legs, tail* and so on. The program has not yet been tested with 
Children, and we arc particularly anxious fa da so during the coming year. We also plan to 
provide for animating :hc ■figures, as. well as developing theoretical maienal to accompany the 
program. Why, for example, does an animal with a carnivores body and an herbivore's head 
"look funny 7 " How could such a creature have evolved 7 

2-4 Music 

2A1 I nsights into Ihe l earning Process 

The wort of the music group tciot a major leap forward this year by/ establishing a small 
satellite lab in a local public school. Telephone, computer terminal and music box together with a 
variety of drums, hells and other instruments were moved Into a room provided by the 1 Martin 
Luther King School in Cambridge. There, J. Bamberger and C Greenberg, a graduate assistant. 
Worked with 4 nine-year-olds (and about S irmslent visiting children) who were turned loose on our 
new materials., new languages and new games. The new content grew out of the previous year's, re- 
thin k I ng of the 'subject matter, iti im plica tjoni for general intellectual development *nd Hi 
interfaces with the larger Logo world. 

A detailed documentation of this, experience ha* proven extraordinarily rich in revealing; 
individual differences between children and ways in which known cognitive structure* come into 
quite unexpected interactions. One out of many hypotheses to account for the richness of events In 
thu experiment is that music is "out of Hep" wuh the general cognitive development of [he 
Children so that [he learning process is able to take a form analogous to cryitallllation from a 
supersaturated solution. Whatever ihc reason, there is no doubt that (bis learning situation I* 
extremely interesting as much (or more!) from the point oT view of intellectual development in 
general as from the narrower paint of view of music education 

2.4.2 Reprss ant tnf Mu si cal Events 

C. Oreenberg has. developed a visual display for music which includes a varic'.y of ways 
for picturing pitch and rime; each of the pictures captures different features and relations of the 
musical structure, sound and picture are generated simultaneously. Next year we hope to 
implement the possibility for a child to actually perform on a drum or keyboard as input to the 
computer, i.e.. performance will generate a real-time display of bo^h picture and sound which will 
remain in computer memory. A mechanical "time machine" which gives the child more "bands on* 
control of the whole process has already been built. W* a|*o want to migrate music and turtle 
animation to show relations between visual and sound transformation processes. 

In another area D. Johnstone, an MIT graduate student, has been developing formal 
models of children's individual strategies for processing simple rhythms. Using the experimental 
result! of Bamberger's work with children, Johnstone is developing the Logo music language to 
make it more compatible with intuitive representations. At the same time he is, working on projects 
and games -+h|ch include powerful tools for procedural music-th inking- this kind of procedural 
thinking extrapolates to building slr-jCures in nrhe? domains, as well. 

Finally, our "center" in the Education Division has attracted a. number pf MIT 
undergraduates through a course (Experimental Studies in Musical Perception arid Learning) 
which pushed the potential of the Lngn muSid system and its underlying thinking well beyond their 
previous limit*. Students obEtived. rheir 0*n and olhc-rf cognitive Strategies in musical problem 
solving (see the paper, "Whar's in a Tune") and also composed rather complex piece* using entirely 
procedural descriptions i>f [he structural relations they wanted. Their copious papers on these 
various projects will be compiled and suimnaiized in a forthcoming article, 

2.5 Games and Simulations 
2,54 Orbit System 

The material an planet^y orhits (see Section 23.1} led to a Logo subsystem and a number 
of games and simulations dealing with orbital mechanics These were designed and implemented 
by A. dlSessa, who will present a descriptive paper in September at the |FIP Second World 
Conference on Computers in Education. We feet that this work it rather unique In that it 
embodies not only an interactive and extensible system for exploring- physics, but also builds upon 
a tAearettccliy different way of presenting this material. 

2.5. 2 Dazzle Dart 

Everyone who Inows the computer woild knows rhe fame spacebar Few games rival 
spacewar in its ability to bold player* in a state of deep concentration and to develop such a 
complex culture of expertise. We would like CO harness such games foi educational use. The 
question arises whether Spaeewar Ls jn some way unique in terms of its fascination for the player. 

Last fall,. H. Abelson, A. dl&eisa and N. Goodman undertook [he goal of designing a new 
computer game that might rival spjeewar in popularity, They succeeded and cceaied a game called 
Daitle Dart This Ls a team game Slmilat to hockey. Instead of hutting a putk, the attacking team 
tries to shine a "beam of light" into a goal. The players control movable mirrors which are usrd IO 
deflect the beam. The rules require teammates to score, not by "direct hits." but by setting up 
reflection patterns among all the players. During January 1-974 the highly successful "First World 
Danle Dart Competition" was held ac MtT. 

While this ii merely a "frivolous game," w? see it as a compelling confirmation that Ch* 
use of computers for highly interactive real-time control represents a pDCentially rich area which 
has hardly been touched hi* educational researchers. 

2.6 Language 

Theoretical work on the religions between Artificial Intelligence, linguistic studies and 
education have become a major theme of worV m the MIT Artificial Intelligence Laboratory and 
In other centers. Several faculty members and gradual sruflen:s here are developing new projects 
using computer* to increase or observe the linguistic abilities of children, tinder a. separate 
NatLonal Institute of Education grant. Professors Papert, Goldstein and M in sky completed a survey 
of recent progress, in Artificial Intelligence theories of language and studied their possible 
application to eduratinn In addition. Profeiior H Sinclair of the University of Geneva will be 
spending the fall term with US as Visiting Professor in the Division for Study and Research in 

Education, and w c expect the theoretical basis Tor our work J n language to be sijrnificantT* 

enhanced through this interaction. ' 

gJLGp als for I 975-75 

Our enemies during; this coming year will be devoted tawarts thoroughly integrating 
fhu new content materia mto our tenching experiments. We expect to see' a number of Joint 
physics-music projects ceniered j round sound generation, 4 great deal of wojk with the new color 
display, and more investigation of "germ lancH ike" introductions to geometry. The umuhrat "build 
*n animal Ji T " wiir be expanded and m Placed vrnh a tablet in order to allow children to create. 
their own "animal parts." Work on animating these creatures will point the way towards an 
elementary "procedural biopsies" (How would you design a sturdy, yet flexible, leg?) as well as 
complement our current material on tropisms. 

We plan to continue our work m language along two dimensions. The first is to develop 
curriculum units for the various natural language projects which *<* have explored in the past, 
including the design of simple queilton-answermg progTams, sentence generators ami parsers. The 
second is to uttliie advanced language comprehension systems developed Of A.L as interfaces to the 
intelligent monitor (Section I.3.2.L) that we plan to implement during the coming year. We *ill also 
interface Logo language projects with a voice generating device. The sophistication and relative 
economy of such devices male them an obvious additional medium in which children can explore 
language (beyond simply teletype interactions). 

3, Experimenting with L&arnlne Environments 

3.1 Qvftrvi&w of Taac;hinE t 1974-75 

About J5 children ringing In age from & to l| spent some rime in the Logo world this 
year. Their wort was supervised by 8 .people, including graduate and undergraduate students., 
Logo suff ant facul:y, Most of rhe children, came form the Martin Luther King and Cambridge 
Alternative public schools. They worked in temporary facilities in the Logo lab except for those 
who were in a satellite lab with the King School (Section Zi\). The children dealt mostly with 
turtle geometry, and this yen r our staff developed new tdejs Tor teaching, for giving children more 
flexibility and for individualizing instruction. 

Staff membm P. Getdenberg and C Solomon invented a number of procedures which 
are "ehlkHemitive" in that they relieve beginners of many of the often frustrating detail of 
programming (See Section! 1.3.1.?- 3.). The fetlTth and fifth graders became quite adept at 
manipulating the basic turtle commands, and did animation projects which had ^mbpdded in them 
the paradigmatic heuristic of debugging, editing* subprocedures. and dealing with input* and 

We have already mentioned S0*ne of the new devices (Section l.l.t) and new computer 
systems. (Sections. U3.1) that were motivated by OUt work with pre -schoolers, through third grade 
students. But hardware and software alone are not sufficient to make the computer environment 
accessible or beneficial to young children. E. Hildrelh. an undergraduate at the lab, is preparing a 
booklet called "Logo for First and Second Gwdw A Teach et's Helper" which is nth In new ways 
of approaching turtle graphics, suggests both basic problems and basic new knowledge that 
children acquire in developing projects and also provides a detailed discussion of "bridging 
activities' between computer concepts and the children's everyday world. ■ 

Techniques for teaching Tim and second graders can also be profitably used In work 
With older Children, as well. For example, a fifth grade child might spend half an hour working 
through what might be the en rue program for a first grader. But even thu brief initial period 
seems to have a substantial effect for some of the children, particularly the "unrnalhematjcar 
<hLldren to whom we have always given special attention. 

3.2 Inter act ions with Fiagolian Psychology 

The Genevan School of genetk epteTwiology is; an important intellectual source for °ur 
point of view. Our project is now at a le^el of development at which it is able to give as well as 
take From Piagetian thinking. Last fall Logo and the Education Division cooperated in inviting 
two students froro Piaget's center, O. de IvfarcelluS and E, Ackermann, to spend a month With Ut. 
Accompanied by 8, Papen. C. Solomon and a number of MIT students. Marcellus and Ackermann 
made daily visits to Cambridge elementary schools where in the Piagetian style, they observed and 
Interviewed young children and nude videoiapes of their experiment s-. The results of these, as 
well as broader issues of developmental psychology, were discussed by the group in a weeily 

S. Wagner a graduate student at Harvard who has also Studied at Geneva, is currently 

interviewing children in Cambridge nursery schools in order to plumb the nature of their 
"linguistic theories;" what's, a word- what's a sentence hew do you know? He has also been 
teaching Logo to & and 9 yenr-okdj with a special eye toward projects which will involve ih* 
children specifically in talking about these things. 

Interactions (with the Center for Generic Epistemotogy in Geneva (Switzerland) will 

continue during I975-7G under joint sponsorship with the Education Division. Two students from 

the Center, C. t>amni and C. Orhenin-Glrard, will again be collaborating with us m the Fall, and 

• H. Sinclair, Profeswr of PsycholmgUistics at th* University of Geneva, wit! be 4 Visiting Profetsor 

at the Education Division. 

3.3 Thft Nflw Lsarnirtq Laboratory 

The lack of adequate non -computer materrals and a Flexible environment in which 
children could take naps or play actively has hampered our teaching experiments ovrr Che past two 
year J. During this lime we have been continually pressing to establish a larger and better designed 
learning environment on the MIT campus. The conduction of such In environment is now 
underway and should toe completed by late' September. 

Beginning » soon as possible {October I) groups of children a^cd 7 through 15 will come 

to the lab on a regular bails. We have an on -gang cornet with teacher* and ad mm 1st ra ton in 

local schools. We have invited them io come with their children ro observe and work, to attend the 

series of lectures which will inmate our own students into wur* in the lab and to keep a running 

dialog" about how their work in the dassrMm can interact with our work in the lab. 

The Pab will include, computer display terminals, a music room, a room for physical skills, 

spaces for devices that are interfaced to Ihe compter {eye-turtle, electric train, airplane seat, etc.) 
and areas for n on -computer "bridge" activities such as block p noting and uuLlding mobiles. This 
will be a major step rewards having Our own learning environment and creating the opportunity 
for children to be much more independent m choosiog their activities and developing long-term 
project*. In addition it provides a real are* for observation, for designing and implementing new 
projects and for teacher training. 

Work in the new learning lab will be a major focus nf activity during the coming year. 
We hope that by the spring semester approximately thirty hour* per w«k can be devoted! to work 
with children from local elementary schools. During this ftnal year of out 3-year contract, w* ,hal! 
particularly concentrate nn refining bn:h uur canjjMei material and OUr presentation. We shall 
also pay particular attemtnn to non -computer "bridge" activities such as those mentioned in Section 
3.1 In addition, teaching activities in the lab will be an integral part of several MIT courses to be 
taught during the coming year (see Sectjon f&) 

3.4 Work with Older Stu dents 

We also worked with high school students and college undergraduates in the Logo 
environment during 1974-75. This is not the major focus *r our teaching activity, but it has 
nevertheless proved to be a valuable complement m our teaching at the elemental y level, it is 
often possible, for example, to test preliminary versions of projects for children by usmr them with 
older students. 

3.4. 1 High Schoo l Stud a nts 

Teaching high school students was done in the summer of ItfH under the auspice* of the 
MIT High School Studies Program in classes led by J. Evans and N. Kowe. Tl,, s .summer It 
Fischer, himself a student introduced to Logo in Rowe's class, ran an HSSP program. Thew 
classes were used to test devices like the light turtle (Section 1.1.1} and the plotter (Section 1.1.6) also. 

Fischer'* class has been experimenting with language and patcem matching (Section (.3.1.51. 

There is ancthcr small group of high school. students who have been using Logo On an 
Informal basis throughout the year. They have turned their attention io computer games, and 
using our Logo system, have been able to design. implement and improve upon games such as 
"ping pon|j" and "moon lander" which are normally only uitd by student! and developed by 

computer professionals. 

3,4,2 CoUeee Urater graduates 

We also experimented this year USiflg Logo as a Coal in MIT undergraduate course?*. 
(Courses ahcal the Logo project are discussed in Section 4.LJ 

3 A 2.1 Mathe matics 

For the past two years r H, Abelson has Taught seminars centered around use of the Logo 
system to MIT mathematics students. In ISfa the classes concentrated on <iou\g mathematics as 
Opposed to teaming about mathematics. This was accomplished through Logo computer projects 
which, although simple from the purely programming point of view, lead quickly and naturally to 
question* for mathematical research. The approach allowed even beginning undergraduates to 
work as creative mathematicians without having to £ir$t master a formidable technical apparatus. 
We expect to repeal this course in 1&7&. and; A- dlSessa plans a similar experiment in physics. Music 

J. Bamberger led a setrunar in which undergraduates used the Logo system in order to 
focus on such questions as- what does it mean to \unttnfami a piece of music? What is tntelttgrnr 
muilcal bthautBT? How does it develop 1 How does it relate to O^her aspects of Intelligent*:? 
Undergraduates obsetved each other in various musical problem-solving activities, formulated 
hypotheses about how the features of a piece generate musical coherence and tewed these via Logo 
and the music box. Computation in the Undsrejaduale Cuf flcuhjg 

Although our work focuses on elementary school science, we believe (hat the kindl of 
ideas we have been developing are equally germane to education at the undergraduate level, and 
that the concentration on "computer-based dialogues" is as limited and short-sighted in the 
university as it is in the primary school. This year we began discussions in this area with other 
educators at MIT. arid alternative, uses of computation In the undergraduate curriculum are 
discussed in a paper in progress by H. Abelson. 

3J.5 Exp eriments in Learning 

gjy^her modynamles S&mtnar 

Durihg Spring Wl\ S. Papert ran a seminar with the goal of understanding why -P 
subject like thermodynamics is universally considered to be among the mosr difficult of the 
undergraduate science curriculum, Could a reformulation of the subject from a procedural 

viewpoint decrease its difficulty for a student? This examination of thermodynamic* Is stJtl 
underway and represents one, of our goals for L07&-I9T6. However. It is WOrlh mentioning here the 
method involved in this enterprise, namely actually studying the subject in a mctajttldent mode. 

The meta refers to a concern in not only solving the probfcms traditionally posed m rembogki, 
but to denrlbe. classify an d diwuis the problem solving strategies used. This approach 
complements nicely [he design of learning environments and we pfcn to apply jt 10 other subjects 
In the coming ^car. ^^ 

3-5.2 Informal Thinkin n Seminar 

The DSRE sponsored a course given jointly by S. Pa pert, B. Snwlsr. D. Schon and S 
Rosenberg which studied the nature of "informal thinking/ as opposed to formal scientific 
problem solving Again the tec hni que was for member* of the seminar to study some new problem 
in meta-studem mode. Typical of the kinds of projetri which students undertook were to learn to 
sketch, to learn how to describe to another the process of untying knots or to learn to Juggle 
There .s n common tore to Informal and Formal Thinking in *i™ of pooler., saving. ntannLng 
and^ debugging techniques. During Hlfe-isra, the course wj|] be given again with the goal of 
making further progress in understanding informal thinking and -developing tecnnlquei for 
thriniing aloud." ^ 

3-6 Go al s for 1975-76 

We conclude wub a more detailed presentation of ou, teaching plans for the canine 
year. Our objectives fall into four broad categories; 

A. Improving our presentation of Logo Ideas. Developing and comparing different 
approaches to work Ln Logo, 

B. Obtaining clearer and more liable observations of children at war* In the Logo 
environment. Bemg nwre precue about the ^ills which children feztn through Lwfl 
activities. "° ^ 

C. Using computational tools and ideas in cognitive research. 

D_ Building an intellectual community. Clarifying prerequisite Skills for doing this kind 
Of research, rnvcsti^.mng issues of teacher training. 

The following nine teaching activities are listed to give Examples of ipcctfu: wavt that w* 
plan to meet -.he above objectives in the coming year. The list n only representative and is not 
intended to be comprehensive. It does not, for example, include anticipated continuation* of our 
worfc at the high school and undergraduate feveh h nor the further development of computer 
devices and new curricula cinaissed in our progress report. 


3JJ L ^av«l5j e in£_^eltflr^^ Planning an d Qabufcainit 

Formulating plans ^d debugging programs have always been two essential component* 
of a child $ Logo experience. But in our teaching, we ourselves have not be*« v er * precis* about 
how one goes about doing these things, flecent research in artificial intelligence has devduped a 
r en vocabulary for describing varmu? type* of planning and debugging sirategiei. One of out 
classes will focus on issues of planning, and especial^ art emp t [rj have children b^.-ne fflort- 
articulate about their plans and planning strategies. 

ftSjJjJgometry on a Grid" a^^temaUv^jrirtrodi^!^ 

hi cut Children Introduced to Logo have begun wjch turtle geometry, drawing picture* and 
animating them. One of OUr classes this year will start with "f-ermland" type programs 11 an 
Introduction to Lugo. This will invoke a differem set of mathematical concept l, For example, the 
notion Of "angle" hardly appears at all, but Issue* concerning interacting ptograms come 
immediately to the forefront. How does this compare with turtle geometry as a source of project* 
for children? Whit new kinds of bugs arise? Haw does this- alternative introduction to Logo 
affect the Jund* of complexities children can deal with in projects? 

3.5.3 An imal B ehavior 

Another class wall be exposed to yet a different alternate introduction to Logo, based on 
procedural models of animal behavior. Question* here will be similar to the ones, listed under 

(3.6-?) above, 

3.6.4 String Figures 

C. Freuder and- G, Iba plan to investigate the Uit of "sculpturing figures out of itrlng" 
(symmography) a* a bridge activity. They will develop a procedural vocabulary for explaining 
this craft tp children and also have the children participate in coordinated computer activities 
{For example, u*mg the computer as a design aid to simulate various possible string figures.) W#. 
also expect to focus, on iisues of how the children move back and forth between the *ab strictness" 
Of the computer simulation and the "reallTy'of the actual materials. ' 

3.6.5 Modi ryiriE Procedure and "Systematic Changes" 

Thi* activity addresses more directly Issues of how Logo work helps develop the capacity 
for "formal thinking". Children will be asked to focus an the relations between the changes they 
make in their procedures and the changes in the procedure does*, to talk explicitly about 

what changes and what remains invariant, and to find strategies for making systematic change*. 
(For example, draw a necklace wj^h round beads on the display Now modify the procedures to 
make every other bead square.} This will be coupled with mure classical Piagetian experiment* 
dealing With Similar i&SUIS- 

3.6.6 Frames of Reference 

This i* another investigation into a component of "formal thinking" which will be 
coupled with piagetian experiments. Children will be glv^n access to Logo environment which 
encourages them to explore Frames, of reference and relative motion. , 

3.6.7 A Psy ch ology lab lor Kids 

A class of children will be taughi to write simple Logo program* which illustrate 

psychological experiments. (Fot example, drawing the frf uller-Lyer Illusion on The display ore 

generaang and testing For recall 'J it-nigs of numbers.'; 

3.6,3 Assembli ng Pictures out ol P arts 

In a *enes of experiments to be conducted by 5. Wagner, children will be given access to 
program* which draw various stand art) i fed eeonwine shapes They will then be asked to assemble 
these into Specific pictures and discuss which parr* are necessary for conducting a given picture.